Problem: If $x \bigtriangledown y = (4-x)(y)$ and $x \veebar y = 4x-6y$, find $(0 \bigtriangledown -1) \veebar -6$.
First, find $0 \bigtriangledown -1$ $ 0 \bigtriangledown -1 = (4-0)(-1)$ $ \hphantom{0 \bigtriangledown -1} = -4$ Now, find $-4 \veebar -6$ $ -4 \veebar -6 = (4)(-4)-(6)(-6)$ $ \hphantom{-4 \veebar -6} = 20$.